“A Rose for Emily” is kind of like the movie “Pulp Fiction” in that the events are told out of order. First create an accurate timeline of the story (Keep this brief--it shouldn't be more than one paragraph!), and then discuss the effect of the narrator’s rearrangement of the order of events on the story and on the reader. To create shock and suspense are some obvious reasons for the rearrangement of events, but there are others too (for example, to build sympathy for Miss Emily). Try to dig deeper to discover these reasons. Remember here that the main focus of your essay is to discuss the effect of the order of the events on the reader, not to just retell the plot.
You may wish to consult the Question Group as there have been questions asked regarding the non-chronological events. Faulkner's shifts in time with the narrator's flashbacks prevent reader from "putting all the pieces together" and thus contributes to the gothic horror of the discovery at the end.
Faulkner's story is divided into five sections, with the first and last dealing with the present, while the three middle sections detail the past. Thus, the story begins and ends with the death of Miss Emily Grierson; the three middle sections cover the time from soon after her father's death and shortly after her "beau," Homer Barron, has deserted her, to the time of her death.
Also, search for the literary device in media res and the uses thereof. By beginning a narrative in the middle, the author creates a single focus that can be developed with flashbacks, etc.
This looks like a good writing assignment, and I'm sure you'll be able to write effectively on this topic. I'm wondering what you want from this discussion, though. This is a forum in which ideas and perspectives are shared, input is given, and questions are answered. You've presented nothing from which we can do those things. Perhaps, if you're looking for any of that, you can try again and see what kinds of responses you might get. As it stands, though, there's not much for us to say.
How does Faulkner uses non-chronological events to achieve a deeper effect further than the obvious shock and suspense?